LIBRARY
OF THE
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
CHOICE OF THE ORGANIZATION
STRUCTURE-
A FRAMEWORK FOR QUANTITATIVE
ANALYSIS OF INDUSTRIAL
CENTRALIZATION/DECENTRALIZATION ISSUES
By
Peter Hammann
633-72
December 1972
MASSACHUSETTS
TECHNOLOGY
50 MEMORIAL DRIVE
BRIDGE, MASSACHUSETTS
INSTITUTE OF
MASS. INST. TtCH.
FEB
DEWEY
10
1973
LIBKAi^Y
CHOICE OF THE ORGANIZATION STRUCTURE:
FRAMEWORK FOR QUANTITATIVE ANALYSIS OF INDUSTRIAL
CENTRALIZATION/DECENTRALIZATION ISSUES
By
Peter Hammann
633-72
December 1972
Thanks are due to Jean Rutherford for kindly and meticulously typing the manuscript.
MAR 7
M.
I.
r.
1973
LIbKARIES
Abstract
Quantitative analysis of centralization/decentralization problems has
so far mainly centered around the question of how decentralization might be
achieved without departing from the system optimum,
techniques of linear and nonlinear models.
involving decomposition
Positive effects, besides
division of labour, of an application of the decentralization principle to
a
firm's organization were not taken into account.
decision model for
leading to
a
In order to do so,
a
hypothetical industrial organization has been developed,
a
comparison of the effectiveness of various more or less decen-
tralized organization structures.
budgeting, where management
performance through
a
is
heuristic routine.
by one or more evaluation criteria,
present achievement,
of the system.
The problem appears to be one in capital
required to generate information of sub-unit
System alternatives may be ranked
the one with highest rank, compared to
indicating steps toward desirable organizational change
For simplicity's sake,
the model,
in a first stage,
has been
conceived as static and deterministic.
This paper is partly based on the author's habilitation theses (14), submitted
to and accepted by the Department of Economics, University of Munich, July
1969 and February 1970, respectively.
Present research has been supported
and the Ford Foundation.
jointly by Technical University of Berlin
I.
What
II.
An overview of related work in Economics,
and Management Science
III.
Some definitions and statements
IV.
The model
is
the issue?
V.
Generation of return functions
VI.
Conclusions and outlook
Operations Research
The principle of task delegation or the division of labour is practically
as old as mankind.
What value can one, then, contribute to
a
quantitative
analysis conducted on the question "is delegation really worthwhile"?, if
generally an affirmative answer has been supposed to be unavoidable?
A
closer look at the problem, however, will reveal several ambiguous underlying assumptions and hazardous generalizations due to some rather one-sided
Let us examine briefly the main pitfalls,
considerations of basic facts.
which led to conclusions that seem to have lived too long, considering the
lack of empirical evidence:
1.
No clear distinction of tasks by their qualitative characteristics
has been made in this context,
thus dealing in an identical fashion with
such different tasks as filling out an order form and the decision on the
order quantity.
From the point of view of delegating task both these show
quite different implications due to quantitative dissimilarities and,
there-
fore, different effects with regard to responsibility for their completion.
2.
Delegation of task requires the evaluation of the various qualities
and capabilities of those person(s) with whom tasks will be shared.
these persons are incompetent,
disastrous.
Likewise,
If
task delegation might well prove to be
their ability to cooperate will enhance or reduce
the efficiency of the work of all concerned.
3.
Not an isolated analysis of the necessity to delegate task at some
particular hierarchical level
is
called for.
Problems of task delegation
can only be dealt with from the system's point of view in order to take
interdependencies of communication and information into account.
to delegate task in some specific way depends on the
The decision
ioint effort of all
-2-
individuals in the system.
is
The quality of
a
single individual's performance
irrelevant.
The various implications of delegation of management task,
especially
4.
decision-making,
have been studied from the system's point of view.
Howevei^,
analysis was conducted under the limiting assumption that the system
optimum
under centralization may not be violated.
Thus, positive effects of task
delegation, possibly leading to
a
higher system optimum were intentionally
neglected.
-
in this
Moreover, managpment
knowledge of the system's structure.
would seem to be quite unnecessary.
context
-
is
assumed to have perfect
Hence, delegation of decision-making
This sadly limiting view may have its
fatal origins in the desire to give some economic
interpretation to
a
well-
known algorithm for decomposing large optimization
models into a set of
sub-models so as to solve them more swiftly and elegantly.
In many analyses,
5.
delegated
is
control over units to which tasks have been
supposed to be exerted by prices, and/or goals and
quota setting.
Control by prices alone has been shown to be
ineffective (7), not least because markets for commodities and services do
not necessarily exist within
firm.
Whether this
structure itself.
is
a
so or not depends largely on the adopted
organizational
Especially, if decision-making
is
delegated,
interdependen-
cies of sub-unit decision processes may
generate "markets" in which outside
control (by central management)
However,
is
required to arrive at decisions at all.
the question remains, whether direct control
media such as prices,
goals or quotas will be accepted by the new
decision-makers.
Therefore, some
subtler indirect control methods or combinations
of direct and indirect methods
seem to be called for which, alas, have not
been investigated so far.
6.
Motivation of individuals to whom tasks have been
delegated
typically,
is,
taken to be granted or irrelevant, when
rigorous control methods
are applied centrally.
The latter may be true in some cases, but
the case
unfortunately, appears to be quite untypical.
itself,
Motivational methods,
therefore, will have to be taken into consideration, though it should be
realized that
-
from the point of quantitative analysis
effects of variations
in
information on the
these methods are extremely scarce.
Centralization of task,
7.
-
in
particular decision-making,
to generate economies of scale for a firm.
is
assumed
This need not be true.
It may
hold in cases of simultaneous central planning.
In
fact,
it
depends on the
completeness and accuracy of information at the central decision-maker's
The second point is that some sort of centralized decision-making
hands.
is
no issue at all for a particular firm.
if any
-
Therefore, economies of scale
-
will have to be achieved in other, more viable or appropriate organ-
ization structures.
8.
The conviction that economies of scale are generally at hand in
centralized systems has led to another conviction:
in such a
control must be exerted
way that these same economies are guaranteed, even when some
(necessary) delegation of task takes place.
Management, therefore, could be
tempted to fake decentralized decision procedures that, eventually, have no
value at all (see also (4) above).
The procedures are time consuming and
costly, possibly offsetting other benefits available.
Moreover, they are
too flimsy not to be understood by recipients of delegation who,
could try to cheat the central decision-maker.
Therefore,
it
in
turn,
seems to be
quite improbable that any real-life organization would work along these lines,
Let us summarize.
Traditional analysis has not centered around the
problem whether decentralization
take place and if so,
in
in
which way.
some particular form,
if ever,
should
Attention has been focussed instead on
the narrow and irrelevant issue, how some quas i-decentralization could be
effected without violating the system optimum.
As
this
is
always known to
management, decentralization appears to be initiated only when some "demo-
.
cratic soothing" of staff is appropriate.
The influences of information,
motivation and possible initiative of sub-unit decision-makers have been
completely ignored.
The task,
therefore, seems to be clear.
The problem
Given that viable alternatives exist, which
should be restated as follows:
organization structure (and hence the degree of decentralization) should
management choose if
it
wants to realize organizational change (see Bennis'
concept (6), pp. 59ff.) in
a
firm?
Finding an efficient, by no means supposedly
optimal, organizational structure for a new firm may be
it
a
second task.
However,
should be tackled, once the somewhat less bothersome first problem has been
We shall try to improve the mentioned defects of earlier
solved satisfactorily.
research by incorporating the notions of information, motivation and initiative
into the decision model.
However, this model should only act as
for more detailed research related to practical applications.
a
framework
At this stage,
we do not know enough about this many-sided problem so as to offer
a
thorough
solution
II.
For completeness' sake let us review very briefly relevant research don«
in
recent years from which one should start in dealing with problems of this
type.
The study that came nearest to the present one and (14) may well be the
one done by Thomas Marschak (28)
.
organizational structures by
time criterion for decision and communication
processes.
Marschak'
s
view,
a
thus,
interest as time considerations,
Tn
is
this he tried to evaluate alternative
a
partial one.
in most real
role when analyzing problems of this kind,
decision criterion.
It
is
of considerable
cases, will play an important
typically involving more than one
Decomposition theory
is
marked by such important papers as those of
Dantzig (10), Dantzig-Wolfe (11), Baumol-Fabian (5), Arrow (1), ArrowHurwicz (2), Charnes-Cooper (8), Charnes-S tedry (9) and Koopmans (20),
(21).
Extensions and discussions on various limitations of the Dantzig-Wolfe model
are given in Hass
who developed
a
(16), Charnes-Clower-Kortanek
(7),
Geoffrion (13), Balas (4)
different algorithm, Kronsio (24) and Ruefli (35).
In the
German literature H. Hax (17) has dealt extensively with the same problem.
Ruefli's paper is of considerable value as it offers
a
goal programming formu-
lation of the decomposition problem without recurring to a global objective
set for the system (which is the starting point in all other papers on
decomposition cited above).
Moreover, his analysis emphasizes the hitherto
ignored fact that the solution from the model, reached after
a
Sequence of
setting goals and prices, depends on the structure of the organization.
Though the well-known implications of goal programming (especially the setting
of goal weights)
limit Ruefli's approach, his results point into a direction
that further research might follow.
Kornai and Liptak (22),
(23)
have tackled decentralized decision-making
by the assumption that management or a central decision unit exert control
over sub-units in response to resource prices generated by the sub-units,
as
might be the case in centrally planned economies.
reformulating the problem as
a
The problem of optimizing
The solution is found by
game.
given organizational structure has been
a
Investigated by Hanssmann (15) as well as, more recently and
fashion, by Mueller-Hagedorn(31)
,
in a
more general
this being the lower-stage problem to the
one under review.
The interested reader is also referred to the ideas and suggestions of
J. Marschak(27),
Radner (33) and McGuire (30) on the theory of teams for the
sake of considering cooperative behavior of individuals in an
organization,
if required.
In
this context,
the system approach, at which this paper aims, has
been most forcefully stressed by Sengupta and Ackoff (36), revealing a
useful proposition on how to control a decentralized system.
Non-quantitative research has been conducted most extensively and the
literature on it
is
far too vast to be listed or commented on here.
Some
particularly relevant findings will be cited later at appropriate instances,
Centralization and decentralization of task are not absolute, but relative
categories.
If we are talking of "decentralization", we should bear in mind
that it is the degree of decentralization
(or centralization") which an organi-
zation has attained or is supposed to arrive at after organizational change
has taken place,
(See Albach
that matters.
(1),
p.
112).
Decentralization,
at least in this context, will be defined as the simultaneous delegation of
task and rights to decide on the task's best ways of accomplishment.
Koontz-O'Donnell (19), pp. 336
ff.). The
(See
primary question will not be how
decentralization may be effected but whether at all and to what degree it
should be realized.
It is clear that there cannot be a normative prescription
of particular organizational structures for firms
methodology aims at providing
a
in general.
The following
framework for individual evaluations.
We shall not deal in great detail with the in terdependencies of organization
structures and information system as has been done by Johnson,
Kast, and
Rosenzweig; (18? pp. 318ff.X Putnam, Barlow and Stilian (32, pp. llff.)or
Richards and Greenlaw (34, pp.
26 7ff-).
However,
there seems to be some
empirical evidence for the argument that an increase in quality and quantity
of information might entail a trend towards centralization of management task.
,
-7-
Let us review more closely the reasons claimed for some sort of decentralization in industrial organizations, as defined above.
on
lower hierarchical levels often stay in
problems than management mostly does,
a
It is because people
closer contact to concrete decision
that they might be given the rights to
decide on the task delegated to them in order to create:
greater sense of responsibility
-
a
-
better motivation
-
a
more intense commitment to their work.
This implies
a
division of labor and responsibility and should result in
-
hopefully, some initiative on behalf of the "new" decision-makers
-
possibly,
(e.g.,
new production, marketing and investment alternatives)
internal economies of scale.
They are facilitated through an increase in quantity and quality of in-
formation which is at the "new" decision-maker's disposal (viz.
more often
-
a
new or
-
improved way of planning) and reflects the closer contact he has
to a particular task.
The main reasoning for an increase in centralization
a
(or,
equivalently
decrease in decentralization), on the other hand, is the belief that the
quality of planning, coordination and control within the organization might
be brought about much more easily when a "central decision unit", whatever
that may be,
takes over or remains in charge.
Apart from that, one hopes
for economies of scale through more efficient resource allocation.
then, are all hypotheses,
is
in
both cases.
These,
What one should not do, however,
to claim for an a-priori empirical and/or theoretical evidence for preferring
one of these (in fact, many) alternatives
(see also, e.g.,
Ruefli (35), pp.
B-513f.).
If one sets out to "compare" different organization structures and
their related decision processes, human behavior emerges as the crucial
and, possibly, most sensitive
parameter
of all.
All human behavior, con-
sciously or subconsciously, appears to be motivated
by the kind or degree
of identification of human beings with their
environment.
far from new.
(See Simon
considered very carefully
to give
(37), p. XVI).
in
However,
this context.
In an
These facts are
they will have to be
industrial organization,
just one relevant example, members of the
central decision unit
will try to motivate subordinate decision-makers
quite deliberately.
is
This
done with respect to management goals and/or
decision alternatives by
means of
a
variety of compensation schemes bound to
accomplishment.
by its recipients.
other hand,
a
(See March-Simon
second time.
certain degree of
(26),
pp.
34f.
and pp. 52f).
On
the
central managment or decision unit should
not feel too confi-
dent about the outcome of this.
need not be,
a
This sort of motivation is certainly
perceived as such
Monetary and other incentives may be, but
taken up by the recipients or they iust work
once and fail the
There exists no such thing in an organization
as built-in
conformity or joint motivation of its members
that might be exploited to
the full when
the need arises.
(See,
e.g., McGregor's theory Y (28), pp. 45f).
Besides these very deliberate forms of exerted
and perceived motivation there
exists
such as
variety of motivational influences which,
typically, will
a
a
elude
organizational alternatives.
They are of
a
body
speculative nature and might best
be described by such homonyms as aspiration
and ambition.
E.g.,
the fact
that some particular task and rights to
decide on it are delegated to
person on
a
central decision unit which might be called
for to decide on viable
a
lower hierarchical level may constitute
(and
a
there is some
empirical evidence for that) some considerable
motivational force though its
impact may,
likewise, diminish again with time.
Analyzing the question
whether and to what degree decentralization
should take place
in an
organi-
zation will have to take such effects
into consideration even if their
-9-
causes may remain unknown, nebulous or vague and even if there may be no
way to influence or control them.
Control,
in
this study, will be effected by budgetary measures.
central management unit allocates
fixed budget to decentralized decision
Budgeting may not be the only way to control an organization.
units.
ever,
a
The
it is a
How-
typical one, which may be encountered in many industrial firms.
If we seek to compare structural alternatives we will have to ensure
comparison will be a reasonably "fair" one.
Introducing
a
that
a
fixed budget for
all the firm's operations in any organizational form may be regarded as
sufficient for the moment.
Thus,
the problem of evaluating more or less
decentralized organization systems appears to be
ing,
problem
a
in
capital budget-
the system alternatives being investment "portfolios" with uncertain
earnings streams.
In these "portfolios",
the decentralized decision-making
units, which themselves control a certain sub-system,
investment alternatives.
represent the various
From these remarks, then, it will be absolutely
clear that the problem at hand can only be solved from the system's point
of view.
Let us illustrate these ideas with the help of
a
simple model which
has been constructed to serve the purpose of demonstration of a methodology.
Let us assume that the firm manufactures
production departments (mtn)
difficulties.
.
m
products in
n
different
The products can be marketed and sold without
Product markets are tangent, but not overlapping.
The pre-
sent organization is such that separate departments for different product
groups have been formed, where all work is done.
Thus, no competition arises
•10-
for
A total budget
jointly needed capacities.
within and outside the firm.
Acquisition of raw materials and other produc-
tion factors shall be assumed as unconstrained.
immediately,
inventories will not build up.
reducing the problem to
a
limits all managerial actions
Its production will be sold
This assumption is a basic one,
An entirely different model would
static level.
have to be developed in order to take dynamic aspects into account.
We are going to compare the following three organizational structures
(see the discussion in
for the decision process
1.
Centralized decison-making by
a
(38),
pp.
130f.):
central decision unit (simultaneous
planning; see Fig. 1).
2.
Decentralized decision-making in functional decision units such as
marketing and production (successive planning, as production decisions
are assumed to depend on prior marketing decisions; see Fig.
3.
2).
Decentralized decision-making in product divisions (simultaneous
planning; see Fig. 3).
A fourth alternative might be considered,
too:
decentralized decision-
making in product divisions with successive planning of marketing and production decisions.
We have left out this alternative somewhat arbitrarily
because coordination and control in organizations such as this seem to be
rather difficult to manage.
However, the list of alternatives could be
augmented without violating the methodological principles which we set out
to demonstrate.
Alternatives
2
and
3
require a-priori management decisions on who
supposed to serve as decision-maker in the decentralized units.
to say,
on paper
the pertinent personnel assignments have to be effected
-
before an analysis can take place.
-
at least
However, it would be possible
to check the problem under consideration with alternative assignment
schedules.
As will be seen,
is
That is
this might prove to be very costly because
-12-
CENTRAL MANAGEMENT
E
Division
Marketing
FINANCE
Division
1
Producti
Marketing
2
Producti
Division
Marketing
control flow
information flow
Fi£^_3:
Divisionally Decentralized Organization Structure
n
Producti
•13-
nearly all of the heuristic routines would have to be repeated many times.
As decision criterion we shall adopt profit or,
to profit generated by the system.
If we restrict ourselves
Probably, Marschak'
stage of the analysis.
,
contribution
to one criterion only we do so because information
on other pertinent criteria is too sketchy as
Whether it represents
applied next.
equivalently
Other criteria might be considered, too.
a
s
to be conclusive at this early
time criterion would be the one
system goal, is
a
matter of discussion.
For simplicity's sake, we shall assume linearity to hold in all functional
relationships.
on values
in
This can be defended,
certain limited ranges.
if variables are allowed only to take
We shall introduce several constraints
to this effect.
In detail, we shall assume that advertising through different media
the only marketing tool.
Market price will be held constant throughout.
firm is supposed to operate well below market saturation.
marketing instruments
is
is
The
Effectiveness of
considered to be discernible without lead time.
Production in the firm starts out from actual orders held over from previous
We shall not deal with problems of obsolescence of machinery, as
periods.
it does not add
significant aspects to the analysis.
It could easily be
integrated into the model if necessity to do so should arise.
Let us put together the model for the firs t alternative
to be a quite conventional mixed
be solved by standard methods
integer
.
It turns out
programming formulation which can
(such as the Brand and Bound Mixed Integer
Programming technique, used in (14) by the author for numerical examples).
Let
(in
vector notation):
p
=
commodity price
c
=
variable production costs per unit
b
=
production capacity
A
=
matrix of technical coefficients
X
=
production quantity
14-
W
=
advertising media quantity
V
=
matrix of advertising effectiveness coefficients
W* =
maximum advertising media quantity
k
=
advertising unit cost
q
=
held over order quantity (to be served according to the FIFO rule)
F
=
fixed cost of the system (independent of decisions)
q* = maximum production quantity
S
=
quantity of added machine aggregates
Z
=
unit capacity of added machine aggregates
g
=
unit cost of added machine aggregates
X
=
attrition cost rate of added machine aggregates
B
=
total budget of the firm (less fixed cost)
Then the objective function
be stated as
of the central
(and only) decision unit can
follows:
4.1 maximize Q^
4.2cx+gs+kw<B
4.3 x<q° + Uw
4.4 x>q
4.5 Ax<b + zs
4 6
.
w^ *
4.7 s<s>v
4.8 X
4.9
,s
s ,w
,w>o
integers
The model for the second alternative
far less detailed and "complete".
,
on the contrary,
two sub-units, one deciding on marketing activities,
operations.
appears to be
In this case, decisions are delegated to
the other on production
For both of these sectors, separate budgets are allocated through
the central decision unit where financial operations and control are retained.
•15-
It seems appropriate to postulate that the "new" decision-maker's should not
be recruited from the central unit's staff if the accent
formation and initiative by decentralized authorities.
members tend to have no better information as individuals.
initiative incorporated in model (4.1
-
4.9)
lies on better in-
Central decision unit
Moreover, the
their's anyway, most of the
is
As marketing decisions have to be observed by the production depart-
time.
Initiative, apart from better or more
ment, successive planning is necessary.
accurate information, may be brought about through the act of decentralizing
as such.
However,
this effect will fade with time.
As we are concerned with
system evaluation, we should suppose that central management will be willing
to implement organizational change
if this appears
to be "worthwhile".
It
may be worthwhile if the gains through decentralization (i.e., by stimulating
initiative) are big enough to offset possible future losses due to decaying
initiative (or, equivalently
,
increasing routine).
We will, at this stage,
not be concerned with the problem of maintaining and stimulating initiative
after organizational change has been carried through.
sight,
to be a
held apart:
limiting proposition.
However,
This may seem, at first
two stages should be clearly
the stage of organizational change and, what may be called,
the
"aftermath" stage.
The second stage will not be entered without having passed
through the first.
If
the a priori outlook for a transition
central management will not be tempted to move.
is
not good enough,
Therefore, we shall devote
research effort to the aftermath stage later on.
If we are
talking of initiative and its stimulation we should bear in
mind where it might be discerned if brought forward.
In our concept
the
following measures could possibly be taken by the new decision-makers:
-
Increasing advertising effectiveness through the creation of
new media or improvements on available media (change of lay-out
or messages).
Of course, an
increase in cost would be the
consequence which, however, might be offset by higher earnings.
Increasing manufacturing productivity through changes in production technology and/or initiation of economies on present
technologies.
Introduction of new products or product lines (if such initiatives
would not have to be checked with central management before taking
such steps).
Additions to machine capacity and similar expandatory measures.
As we have noted earlier, better and more detailed information might be
exploited,
This will lead to two, possibly intertwined, effects:
too.
A new decision-maker may view the decision problem the same way
as the central unit does.
However, parameters will take on dif-
ferent values.
A new
decision-maker has an entirely different view of the decision
problem's structure as compared to that taken by the central
management unit (e.g., differences
in
perception of the nature
of certain functional relationships").
From this follows that, contrary to the first of our alternatives, central
management will have only
performance.
Therefore,
a
limited and rather vague knowledge of sub-unit
it will be
forced to experiment on it or estimate
subjectively the possible outcomes of an organizational change.
Let us further assume that management tries to motivate sub-unit decision-
makers by means of some profit sharing.
in
this case:
a
Thus, we have two ways of motivation
monetary (i.e., profit sharing) and
the act of decentralizing as such).
non-monetary one (i.e.,
Monetary motivation through some sort of
profit sharing is quite common because it
and initiative motivation.
a
is
directed towards goal motivation
As we have noted earlier, however,
it
may not work.
But we shall adopt it as a first hypothesis on central management action.
The
17-
rate of profit shared with sub-unit decision-makers will be assumed to be
equal for all units throughout in order to exclude bargaining among them.
We are now in
a
position to formulate the models for the remaining two
decision alternatives.
Let us begin with functional decentralization
initiative in any of the two departments,
,
where
typically, will be counterchecked
by the other in not following up for some reason (see Enthoven's comment on
control of functionally decentralized systems (12), pp. 396ff.)'
Let
)
=
actual advertising expenditures
fr,(B„)
=
contribution to profit by the production department,
g*(B-.)
=
f
(B^
dependent on
optimum allocation of promotional expenditures
Therefore f^(By) should be replaced by the notation f„i|B„|
g''<-(B^ )
^
=
marketing and production budgets, respectively
B
=
total budget of the firm,
F
=
fixed system cost
C
=
vector of variable production costs per unit
q
=
vector of orders held over from earlier periods (to be
fh
=
profit share rate
B,
B„
identical to B in 4.2
served according to the Fifo rule)
cost factor) granted to sub-unit
(a
decision-makers
Then the objective function reads as follows:
4.10
4,
Maximize Q^
=
(1"
^
^
[
^
2
{
^^2
^''
I
''^l^l'
"
'^I'^'^l^
^Isubiect
cussion on how to obtain these
the moment.
We shall,
f unctions
experimentally or by estimation
instead, proceed to write down
tf^e
foi
model for the third
alternative (divisional decentralization), for which
we hold the important
(and no doubt,
limiting) assumption that the organization
of the firm may be
broken down into independent divisions.
Then let:
contribution to profit of division P (P = 1^--h)
"
^p^'^p-'
Cp
=
vector of variable costs per unit of division
q
=
vector of orders held over from earlier
periods in
p
P
division P (to be served according to the Fifo
rule)
The other symbols are retained from the model
for the second alternative.
Then the obiective function can be written as
follows:
H
4.14
Maximize Q
=
(i
-
/))-)
L
subject to
4.15
H
i
P
>
-
C q o
P P
As can be readily seen, models
f,
1'
Again,
P
P
1
4.17
common.
1
B
P =
4.16
I
P =
f^
(P =
1,---, H)
(P =
1,---, H)
(4.10
-
4.13) and (4.14
-
4.17)
h ave
much in
would have to be known for comparison of
alternatives,
Let us now turn to the important question
of how the unknown return functions
ot
and f
respectively, can be obtained.
There are, basically, two w..ys:
2,
p
f„
-
Experimentation
Estimation
19-
the situation faced by the central decision unit is a completely new
As
one no historical data will be available as a preliminary guideline.
Experimentation in both alternatives two and three means that return
functions would have to be established iteratively and heuristically
a
priori optimal allocation of the budget will be impossible.
An
.
For alternative
two one might proceed as follows:
Step
1:
Set budgets B, and B„ arbitrarily, however, observing restrictions
(4)
and
(12).
This could perhaps, also be done according to the
financial requirements of both departments in the last period,
which would have to be calculated post festum from secondary
historical data.
Transmit budget information to the marketing and production sub-
Step
2:
Step
3:
Step
4:
Transmission of optimal marketing plan to the production department.
Step
5:
Optimization of production goals.
unit decision-makers, selected previously.
Optimization of marketing goals.
At this stage we may distinguish
four cases:
(a)
B^
and B„ are fully used up.
(b)
B
is
fully used up, B„ only partly.
(c)
B.
is
only partly used up.
(d)
B,
and B„ are only partly used up.
B„ fully.
Therefore we have
Step
6:
Information of central management on total profit contribution
of the system and the financial status of the functional departments,
Central management may accept the arbitrary budget allocation as "optimal"
if
(a)
holds.
the firm
-
a
In case of
(d)
management should cut down the total budget of
very unlikely situation, however.
In cases
(b)
and (c)
a
re-alloca-
tion of budgets seems promising and central management might be tempted to do so.
Thus, one goes back to Step
if
1
and repeats the routine.
reallocations fail to bring additional gains,
or somewhere near to it.
times,
i.e.,
Iterations terminate
if we arrive at
(a)
It is possible to set budgets arbitrarily several
thus again obtaining points of the return function.
These we can
plot in both cases and a continuous curve may be fitted to the data, subsequently.
However, as these experiments will be rather costly, central man-
agement might be well advised to follow the above routine.
on
the other hand,
to perform some
during the first round.
It
is
It can be necessary,
iterations if one arrives at (a) already
important to keep in mind that the return
functions will constitute some much needed information for future planning
at
the aftermath stage.
Let us summarize the information flow in the system:
Central Management
Marketing
Production
Central
Management
Marketing
Production
±El1_±:
Total Advertising Expenditures
Marketing
Investment
Expendi tures
Total contribution
to Profit
Minus Attritions Costs
Total Variable Production Costs
Production
Investment
Expenditures
Information Flow in
a
Optimal
Marketing
Plan (Market
Constraints)
(Planning
Deadlocks)
Functionally Decentralized Organizati(
-21-
It should be noted that not all information emerging from the departments
will be transmitted to central management.
be necessary and sufficient.
The above information appears to
As the experiment shows some features of a real-
world business game some psychological implications should not be overlooked.
The designated sub-unit decision-makers may develop some routine when the
experiment is run too often.
Moreover, they may be tempted to fake initiative
and pretend to have better and more information than they actually do.
Hence,
the experiment will have to be handled very delicately in order to avoid any
such bias.
Much the same sort of reasoning applies to the generation of return
functions for alternative three
The process is simplified as there will be
.
simultaneous decision-making on production and marketing plans.
The steps
are now the following:
Step
1:
Set budgets B
In this case,
arbitrarily, observing constraints 4.15 and 4.16.
however, there will probably not be some sort of
advance or historical information on actual financial requirements in the divisions.
Transmit budget information to pre-selected division decision-
Step
2:
Step
3:
Optimization of division goals.
Step
4:
Information of central management on divisional profit contrib-
makers
.
ution and financial status.
As can be easily seen,
independence of divisions reduces the information
Again, central management may accept any
flow in the system to a minimum.
(more or less) arbitrary budget allocation as "optimal" if budgets are all
used up in the divisions.
One might stop repeating the experiment, possibly,
when results turn out iust to be
a
near miss of the "optimum".
In all other
cases, central management will be tempted to arrange budgetary shifts where
•22-
indicated to arrive at a different and, hopefully,
more auspicious budget
allocation.
Iterations terminate when no shifts are possible or
seem to
be called for.
The second way to arrive at sub-unit return
functions is, of course,
some form of subiective estimation
which could be helpful to
a
There may be a variety of "clutches"
.
manager seeking to arrive at reliable estimates.
Little (25) has offered some suggestions how to
do it which we can apply in
this context,
hand.
too,
if some knowledge of the system's past
performance
put of sub-units under budgeting.
at
The return functions will approach saturation
levels asymptotically as budget volumes increase
(Fig. 5).
b
Fl£^_5:
is
We may assume that some law of diminishing
returns holds for the out-
S
Idealized sub-unit response on return function,
.
.
.
-23-
This response or return curve may be determined by four points:
If budgets are reduced to zero,
During the preceding period,
there will be no returns (P^
the sub-unit
)
(under centralized
decision-making) put out f'(B') on the basis of
a
budget B*.
Central management, therefore, may hold the hypothesis that
a
similar performance should be expected under the adopted form
of decentralization
(P„)
Central management might ask for the necessary budget B if
increase in returns over f'(B') was to be achieved (P
507„
Central management will feel that there exists
level f*(B) which constitutes
a
a
a
)
saturation
maximum limit to sub-unit
output (P,).
Through the four points we can fit
a
smooth curve as in Fig.
5.
Algebraically, the curve would be of the following form:
5.1
=
f(B)
f-.v(B)
B^
2_^
•
oC
Where
+
B^
and r are constant parameters, reflecting central management's
'^^
expectations on the power and nature of decentralization response.
that for
B
=
0,
also
=
f(B)
Not(
0.
VI.
We have tried to provide
organizational choice.
a
framework for quantitative analysis of
The method has been shown with the help of three
distinct structural alternatives:
centralized decision-making
functionally decentralized decision-making
-
divisionally decentralized decision-making in contrast to earlier
:
.
•24-
research,
the following important notions have been considered in
the approach:
quality and quantity of information
motivation
initiative
on behalf of sub-unit decision makers.
allocation.
Control is exerted through budget
Point of view for the analysis has been the system.
As we have dealt primarily with methods,
not results from the analysis,
there may be room for a number of possible extensions.
Here is
a
list of
those which appear to be particularl/ fruitful for subsequent research and
applications
1.
Dynamic modelling of the problem.
To this purpose it might be
useful to delegate management task, but not decision-making.
Over
several periods, then, the system's behavior could be studied,
leading to a better understanding of work interaction at sub-
central levels.
With these results at hand,
a
decision of altering
the decision process might be better supported.
2.
Stochastic modelling of sub-unit response to management's motivational
methods
3.
Experimentation on the effects of other motivational methods than
4.
Study of the adaptive properties of control, possibly in conjunction
profit sharing and decentralization of authority.
with research done under position (1).
5.
Study of interactions
bet\.'een
divisions with regard to information
flow and resource bargaining.
6.
Investigations of initiative maintenance at the aftermath stage.
Methods that spring to mind, in this context, are management training
and post-experience studies.
-25-
7.
Improvements on experimental design for information gathering
sub-unit performance.
.
,
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Date Dui
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